Multiscale Modeling of a Germanium Quantum Dot in Silicon
A method is described for multiscale modeling of a quantum dot in a semiconductor solid containing a free surface. The method is based upon the use of lattice-statics and continuum Green’s functions integrated with classical molecular dynamics. It fully accounts for the nonlinear discrete lattice effects inside and close to the quantum dot, discrete lattice structure of the host solid near the quantum dot and reduces asymptotically to the macroscopic continuum model near the free surface. Our method can model a large crystallite containing, for example, a million atoms without excessive CPU effort and it connects nanoscales seamlessly to macroscales. The method relates the physical processes such as lattice distortion at the atomistic level to measurable macroscopic parameters such as strains at a free surface in the solid. The method is applied to calculate the lattice distortion around a Ge quantum dot in Si. Preliminary numerical results are reported.
Key wordsgermanium in silicon lattice Green’s functions molecular dynamics multiscale modeling quantum dots
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- 3.Thomson R, Zhou S, Carlsson AE, Tewary VK. “Lattice imperfections studied by use of lattice Green’s functions”, Phys. Rev., B46, 10613–10622, 1992.Google Scholar
- 7.Tadmor EB, Ortiz M, Phillips R. “Quasicontinuum analysis of defects in solids”, Phil. Mag., A73, 1529–1563, 1996.Google Scholar
- 8.Rao S, Hernandez C, Simmons JP, Parthasarathy TA, Woodward C. “Green’s function based boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations”, Phil. Mag., 77, 231–256, 1998.Google Scholar
- 10.Tewary VK. “Multiscale Green’s-function method for modeling point defects and extended defects in anisotropic solids: application to a vacancy and free surface in copper”, Phys. Rev., B69, article number 094109, 2004.Google Scholar
- 12.Tewary VK. “Computationally efficient representation for elastostatic and elastodynamic Green’s functions for anisotropic solids”, Phys. Rev., B51, 15695–15702, 1995.Google Scholar
- 14.Yang B, Tewary VK. “Formation of a surface quantum dot near laterally and vertically neighboring dots”, Phys. Rev., B 68, article number 035301, 2003.Google Scholar
- 15.Baskes MI. “Modified embedded-atom potential for cubic materials and impurities”, Phys. Rev., B46, 2727–2742, 1993.Google Scholar